Analysis of K-fold Cross Validation

I'm in a machine learning class right now and having difficulty with some problems.

I'm pretty much trying to figure out the correlation between model coefficient estimates over different folds during cross-validation.

The assumption of the model is Y = β + e such that E(e) = 0, Var(e) = σ^2.

If we use K-fold CV, how can I determine the correlation between the least sq. est of β estimate using the first fold and the least sq. est of β estimate using the second fold?

I know since β_1 = 0 by the model assumption, the estimate of β is just the mean of the observations. And I know that as K goes towards n (n = # of observations), the correlation will increase as both training sets will have more and more overlap. I'm just unsure where to start to derive the exact correlation.